Lemma 2.4  ([1]})
Let \(G\)  be a \(k\) -connected graph, let \(x\)  be a vertex of \(G\)  and let \(Y\subseteq V(G)\backslash \lbrace x\rbrace \)  be a set of at least \(k\)  vertices of \(G\) . Then there exists a \(k\) -fan in \(G\)  from \(x\)  to \(Y\) , that is, there exists a family of \(k\)  internally disjoint (\(x,Y\) )-paths whose terminal vertices are distinct in \(Y\) .

